Gallavotti, G., Universita degli Studi di Roma "La Spienza", Rome, Italy

Foundations of Fluid Dynamics

2001. XII, 523 pp. 41 figs., 1 tab., 399 problems. Hardcover
3-540-41415-0

This monograph on fluid mechanics is not only a superb and unique textbook but also an
impressive piece of research. The author writes from the vantage point of a mathematical physicist:
Having in mind the important applications and approximation techniques used in physics in
engineering, he carefully analyses the power of the theory. He treats, among others, the theories of
Leray, Ruelle and Takens, and discusses Lorenz's ideas of attractors. This is the only textbook
that fully covers turbulence, all the way from the works of Kolmogorov to modern dynamics.

Keywords: Fluid Dynamics, Turbulence, Attractors .

Contents: From the Contents: Continua and Generalities About Their Equations.- Empirical
Algorithms. Analytical Theories.- Analytical Theories and Mathematical Aspects.- Incipient
Turbulence and Chaos.- Ordering Chaos.- Developed Turbulence.- Statistical Properties of
Turbulence.- Bibliography.- Name Index.- Subject Index.- Citations Index.

Series: Texts and Monographs in Physics.

Murray, J.D., University of Washington, Seattle, WA, USA

Mathematical Biology 3rd ed.
Spatial Models and Biomedical Applications

3rd ed. 2001. Approx. 810 pp. Hardcover
0-387-95228-4

In the ten years since the first edition of this book appeared the field of mathematical biology has
grown at an astonishing rate and has established itself as a distinct discipline. Mathematical
modelling is now being applied in every major discipline in the biomedical sciences. Though the
field has become increasingly large and specialized, this book remains important as a text that
introduces some of the exciting problems that arise in biology and gives some indication of the
wide spectrum of questions that modelling can address. Due to this tremendous development in
recent years, for this new edition Murray is covering certain items in depth, giving new applications
such as modelling marital interaction, growth of cancer tumours, temperature sex determination,
wolf territoriality, wolf-deer survival etc. In other areas he discusses basic modelling concepts and
provides further references as needed. He also provides even closer links between models and
experimental data throughout the text. The book continues to present a broad view of the field of
theoretical and mathematical biology and gives us an excellent background from which to begin
geniune interdisciplinary research in the biomedical sciences.

Keywords: Mathematical Biology, Mathematical Modelling in Biology

Contents: 1 Continuous Population Models for Single Species * 2 Discrete Population Models for Single Species * 3 Models for Interacting Populations * 4 Temperature-Dependent Sex Determination (TSD) and
Survivorship * 5 Modelling the Dynamics of Marital Interaction: Divorce Prediction and Marriage Repair * 6 Reaction Kinetics * 7 Biological Oscillators and Switches * 8 Belousov-Zhabotinskii Oscillating Reaction * 9 Perturbed and Coupled Oscillators and Black Holes * 10 Dynamics of Infectious Diseases: Epidemic Models and AIDS * 11 Reaction Diffusion, Chemotaxis and Non-local Mechanisms * 12 Oscillator Generated Wave Phenomena and Central Pattern Generators * 13 Biological Waves: Single Species Models * 14 Biological Waves: Multi-Species Models * 15 Spatial Pattern Formation with Reaction Diffusion Mechanisms * 16 Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms * 17 Modelling the
Spatial Patterning of Tooth Primordia in the Alligator * 18 Complex Bacterial Patterns and Chemotaxis * 19 Mechanical Theory for 1= Generating Pattern and Form in Development * 20 Evolution and Developmental Constraints * 21 Angiogenesis: Network Formation in

Series: Interdisciplinary Applied Mathematics.VOL. 200

Robert, C.P., Universite Paris Dauphine, Paris, France

The Bayesian Choice
From Decision-Theoretic Motivations to Computational

2nd ed. 2001. Approx. 455 pp. Hardcover
0-387-95231-4

This graduate-level textbook presents an introduction to Bayesian statistics and decision theory. Its
scope covers both the basic ideas of statistical theory, and also some of the more modern and
advanced topics of Bayesian statistics such as complete class theorems, the Stein effect,
Bayesian model choice, hierarchical and empirical Bayes modeling, Monte Carlo integration,
including Gibbs sampling and other MCMC techniques.
The second edition includes a new chapter on model choice (Chapter 7) and the chapter on
Bayesian calculations (6) has been extensively revised. Chapter 4 includes a new section on
dynamic models. In Chapter 3, the material on noninformative priors has been expanded, and
Chapter 10 has been supplemented with more examples. The Bayesian Choice will be suitable
as a text for courses on Bayesian analysis, decision theory or a combination of them.
Christian P. Robert is Professor of Statistics in the Applied Mathematics Department at the
Universit・Paris Dauphine, and external lecturer at Ecole Polytechnique, Palaiseau, France. He
was previously Head of the Statistics Laboratory at the Center for Research in Economics and
Statistics (CREST) of the National Institute for Statistics and Economic Studies (INSEE) in Paris.
In addition to many papers on Bayesian statistics, simulation methods, and decision theory, he
has written three other books, including Monte Carlo Statistical Method (Springer 1999) with
George Casella. He also edited Discretization and MCMC Convergence Assessment (Springer
1998). He has served or is serving as an associate editor for the Annals of Statistics, the Journal of
the American Statistical Association, Statistical Science, and Sankhya. He is a fellow of the
Institute of Mathematical Statistics, and the Young Statistician Award of the Socite・de Statistique
de Paris in 1995.

Contents: Decision-theoretic foundations of statistical inference.- From prior information to prior
distributions.- Bayesian point estimation.- Tests and confidence regions.- Bayesian Calculations.-
Model Choice.- Admissibility and complete classes.- Invariance, Haar measures, and equivariant
estimators.- Hierarchical and empirical Bayes extensions.- A defense of the Bayesian choice.

Series: Springer Texts in Statistics.

Spencer, J., New York University, NY, USA

The Strange Logic of Random Graphs

2001. X, 160 pp. 15 figs. Hardcover
3-540-41654-4

The study of random graphs was begun by Paul Erdos and Alfred Renyi in the 1960s and now has
a comprehensive literature. A compelling element has been the threshold function, a short range in
which events rapidly move from almost certainly false to almost certainly true. This book now joins
the study of random graphs (and other random discrete objects) with mathematical logic. The
possible threshold phenomena are studied for all statements expressible in a given language. Often
there is a zero-one law, that every statement holds with probability near zero or near one. The
methodologies involve probability, discrete structures and logic, with an emphasis on discrete
structures.
The book will be of interest to graduate students and researchers in discrete mathematics.

Keywords: graph theory, combinatorics, probability, random graphs

Contents: Part I. Beginnings.- 0. Two Starting Examples.- 1. Preliminaries.- 2. The Ehrenfeucht
Game.- Part II. Random Graphs.- 3. Very Sparse Graphs.- 4. The Combinatorics of Rooted
Graphs.- 5. The Janson Inequality.- 6. The Main Theorem.- 7. Countable Models.- 8. Near Rational
Powers of n.- Part III. Extras.- 9. A Dynamic View.- 10. Strings.- 11. Stronger Logics.- 12. Three
Final Examples.- Index.

Series: Algorithms and Combinatorics.VOL. 22

Kiehl, R., University of Mannheim, Germany
Weissauer, R., University of Mannheim, Germany

Weil Conjectures, Perverse Sheaves and l'adic Fourier Transform

2001. Approx. 350 pp. Hardcover
3-540-41457-6

In this book the authors describe the important generalization of the original Weil conjectures, as
given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the
important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's
theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this
framework Deligne's results on global weights and his notion of purity of complexes obtain a
satisfactory and final form. Therefore the authors include the complete theory of middle perverse
sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and
simple proofs. To round things off, there are three chapters with significant applications of these
theories.

Keywords: Etale cohomology, generalized Weil conjecture, Deligne ' s theory of weights and of
purity, middle perverse sheaves, Deligne ' s Fourier transform, Hard Lefschetz Theorem, estimates
of exponential sums, Springer representations Weyl groups .

Contents: The general Weil conjectures (Deligne's theory of weights).- The formalism of derived
categories.- Perverse sheaves.- Lefschetz theory and the Brylinski-Radon transform.- Trigonometric
sums.- The Springer representations.

Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge .VOL. 42